Algebra worksheet — GCSE Foundation

1.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

2.Which expression means the same as a × a × a?

3.Which of these equations describes a vertical line?

4.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

5.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

6.Write down the expression that means the same as p + p + p + q.

7.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

8.Make m the subject of the formula w = m − 8.

9.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

10.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

11.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

12.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

13.Which of these is an expression?

14.Work out the distance of the point (−6, 4) from the x-axis.

15.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.